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Marginal Stability and the Metamorphosis of BPS States

Adam Ritz, Mikhail Shifman, Arkady Vainshtein, Mikhail Voloshin

Abstract

We discuss the restructuring of the BPS spectrum which occurs on certain submanifolds of the moduli/parameter space -- the curves of the marginal stability (CMS) -- using quasiclassical methods. We argue that in general a `composite' BPS soliton swells in coordinate space as one approaches the CMS and that, as a bound state of two `primary' solitons, its dynamics in this region is determined by non-relativistic supersymmetric quantum mechanics. Near the CMS the bound state has a wave function which is highly spread out. Precisely on the CMS the bound state level reaches the continuum, the composite state delocalizes in coordinate space, and restructuring of the spectrum can occur. We present a detailed analysis of this behavior in a two-dimensional N=2 Wess-Zumino model with two chiral fields, and then discuss how it arises in the context of `composite' dyons near weak coupling CMS curves in N=2 supersymmetric gauge theories. We also consider cases where some states become massless on the CMS.

Marginal Stability and the Metamorphosis of BPS States

Abstract

We discuss the restructuring of the BPS spectrum which occurs on certain submanifolds of the moduli/parameter space -- the curves of the marginal stability (CMS) -- using quasiclassical methods. We argue that in general a `composite' BPS soliton swells in coordinate space as one approaches the CMS and that, as a bound state of two `primary' solitons, its dynamics in this region is determined by non-relativistic supersymmetric quantum mechanics. Near the CMS the bound state has a wave function which is highly spread out. Precisely on the CMS the bound state level reaches the continuum, the composite state delocalizes in coordinate space, and restructuring of the spectrum can occur. We present a detailed analysis of this behavior in a two-dimensional N=2 Wess-Zumino model with two chiral fields, and then discuss how it arises in the context of `composite' dyons near weak coupling CMS curves in N=2 supersymmetric gauge theories. We also consider cases where some states become massless on the CMS.

Paper Structure

This paper contains 23 sections, 147 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Soliton Dynamics near the CMS
  3. Dominant interactions
  4. The restructuring mechanism
  5. Embedding of SQM within the field theory superalgebra
  6. An ${\cal N}=2$ WZ Model in Two Dimensions
  7. Introducing the model
  8. Decoupled solitons, $\mu = 0$ case
  9. Stabilization by $\mu$
  10. A loosely bound composite BPS state
  11. Quantum Mechanics of Two Solitons
  12. SQM superpotential from field-theoretic supercharges
  13. Properties of the two-soliton system
  14. Another dynamical regime: Extra Moduli on the CMS
  15. Dyons in SU(3) ${\cal N}=2$ SYM
  16. ...and 8 more sections

Figures (10)

  • Figure 1: A schematic representation of the moduli space for ${\cal N}\!\!=\!2\;$ SYM with gauge group SU(2) in terms of the vev $u=\langle{\rm tr}\,\phi^2\rangle$ of the adjoint scalar $\phi$. The $W$ bosons only exist outside the shaded region, which consequently determines their stability domain.
  • Figure 2: The potential $V(x)$ in the problem (\ref{['wqm']}), (\ref{['toysp']}) (solid line) and the corresponding ground state wave function (dashed line). The parameter $\mu =0.98$. The units on the vertical and horizontal axes are arbitrary.
  • Figure 3: Structure of vacua and solitons in the ${\rm Re}\, u$, ${\rm Re}\, v$ plane for real $\nu$ and $\mu$ .
  • Figure 4: The curve of marginal stability in the complex plane of $\nu$.
  • Figure 5: The domains of stability for the composite BPS states (shown for $\mu_2=0.2$). The hatched region along the real axis is the stability domain for the $\{1,1\}$ solitons and its antiparticles, in the cross hatched one the $\{1,-1\}$ solitons and its antiparticles are stable.
  • ...and 5 more figures